Question: Simplify the following expression: $t = \dfrac{p^2 - 12p + 27}{p - 9} $
Solution: First factor the polynomial in the numerator. $ p^2 - 12p + 27 = (p - 9)(p - 3) $ So we can rewrite the expression as: $t = \dfrac{(p - 9)(p - 3)}{p - 9} $ We can divide the numerator and denominator by $(p - 9)$ on condition that $p \neq 9$ Therefore $t = p - 3; p \neq 9$